Power Response

On-axis is the red beam aimed at you; power response (blue) is every arrow summed. The gap between them is the Directivity Index.

What it is

The total sound energy a speaker radiates into the whole room across all angles, summed per frequency.

Key facts

• Speed of sound in air is 343 m/s at 20 degrees C (about 1235 km/h); it rises roughly 0.6 m/s per degree C.
• On-axis (anechoic) response = sound straight ahead; power response = energy averaged over the full sphere (4 pi steradians, the whole 360 degrees).
• Directivity Index (DI) in dB = On-axis response minus Power response. DI = 10 x log10(Q), where Q is the directivity factor.
• Q (directivity factor) = how much louder on-axis is vs an omni source of the same total power. Omni = Q1, DI 0 dB. A hemisphere = Q2, DI +3 dB.
• Directivity rises with frequency: a box that is omni in the bass beams in the treble, so power response usually tilts DOWN with frequency even when on-axis is flat.
• Smoothly rising DI (1-3 dB per octave) sounds natural; sudden jumps or dips in DI = audible tonal colour from the reflected field.
• Doubling acoustic power = +3 dB (10 x log10(2) = 3.01 dB). +10 dB needs 10x the power and sounds about twice as loud.
• -3 dB = half power (the half-power / -3 dB point sets a driver's usable beamwidth and a crossover frequency).
• Sound pressure level: doubling pressure (voltage) = +6 dB (20 x log10(2) = 6.02 dB).
• Inverse-square law: in a free field SPL drops 6 dB per doubling of distance. In a reverberant room, beyond critical distance level stops dropping and power response dominates what you hear.

How it works

1. Drive the speaker and measure SPL at many angles around it (a full sphere of mic positions).
2. Convert each angle to energy (power), weight by the area of sky it covers, and sum across all angles.
3. Plot that summed energy against frequency = the power response curve.
4. Subtract power response from on-axis response to get the Directivity Index (DI) curve.
5. Read the tilt: a smooth gentle DI rise = even, natural room sound; lumps = harsh or dull patches.

Real examples

• A flat-on-axis tweeter that beams at 10 kHz still sends weak high-end sideways, so the reflected field sounds dull even though the direct sound measures flat.
• A waveguide/horn keeps Q roughly constant (constant-directivity), so on-axis and power response stay parallel and the room stays tonally even.
• A wide-dispersion dome at 16 kHz lights up side walls with treble, making a live, glassy reverberant field; a narrow ribbon does not.
• A subwoofer is omnidirectional (Q approx 1) below about 100 Hz, so its power response and on-axis response are nearly identical.
• Two speakers with identical on-axis curves can sound completely different in a real venue purely because of different power response.

How it helps in live sound

• Choose constant-directivity horns/line arrays so DI stays smooth; the reflected field then matches the direct sound and EQ behaves.
• Don't fix a dull room with on-axis EQ alone; if the box beams highs, boosting treble at the desk just hardens the direct beam, not the room.
• Aim coverage so hard reflective walls/ceiling get the LOW-DI (wide) part of the response, reducing harsh slap-back.
• Use the speaker's -6 dB horizontal/vertical coverage angle (off datasheet) to plan overlap and avoid uneven power build-up.
• In big reverberant halls work inside critical distance: get the audience in the direct field, because past it the power response (room) takes over.
• Measure with a moving-mic or spatial average (not one on-axis point) so your trace reflects power response, the thing the audience actually hears.